Question

There's one triangle satisfying angle BCA = 60 degree, AB = 12 and AC = 10 shown below:

The only possible value of BC is a, as shown above. What is a?

Answer 1

Answer:a = 13.31

Explanation:

Answer 2

13.3

Explanation:

draw a line from A to be perpendicular to line BC

which will cut a into 2 parts. call it a1, & a2

so now you have 2 right angle triangle - left side one with an angle known 60°, which means the top angle after the separation is 30° & something else, we don't care that part.

any right angle triangle with 30-60-90 ° has a property of shorter side = 1/2 of the long side. so right away we know a1= 5. and the perpendicular line = 5√3. this property you should memorize.

now solve a2. look at the triangle on the right.

because we know the perpendicular line is 5√3, and long side =12

so (a2)² = 12² - (5√3)² =144-75 =69

so a2 = 8.3

so a = a1+a2 = 5+8.3 =13.3